Solve for $x$ and $y$ using elimination. ${-4x+6y = 26}$ ${-5x-5y = -55}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-4$ ${-20x+30y = 130}$ $20x+20y = 220$ Add the top and bottom equations together. $50y = 350$ $\dfrac{50y}{{50}} = \dfrac{350}{{50}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-4x+6y = 26}\thinspace$ to find $x$ ${-4x + 6}{(7)}{= 26}$ $-4x+42 = 26$ $-4x+42{-42} = 26{-42}$ $-4x = -16$ $\dfrac{-4x}{{-4}} = \dfrac{-16}{{-4}}$ ${x = 4}$ You can also plug ${y = 7}$ into $\thinspace {-5x-5y = -55}\thinspace$ and get the same answer for $x$ : ${-5x - 5}{(7)}{= -55}$ ${x = 4}$